Calculation of Electric Field with Various Charge Distributions
Calculation of electric field for different charge distributions, including a long insulating rod with varying charge densities surrounded by conducting cylinders. Understand how the electric field magnitude varies based on the setup and charge distribution parameters.
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What is the charge enclosed? core: 1, radius a thin shell: , radius b thick shell: 2, radii c & d Gaussian sphere, radius r ( )r2 4 3pa3r1+4pb2s + 4 3pr3-4 3pc3 Find E at radius r: 3p r3-c3 ( )r2 )r2 e04pr2E =4 3pa3r1+4pb2s +4 ( ) 1 ( E = 3e0r2a3r1+3b2s + r3-c3
Take a very long insulating rod, radius a=0.05m and charge density =60 C/m3, surrounded by a conducting hollow cylinder of inner radius b=0.10m and outer radius c=0.15m. What is the magnitude of E at a < r < b? e0FE= qenc )= r p a2h ( ( ) h e02p r hEr r Er=ra2 2e0r (60mC/m3)(0.05m)2 2(8.85 10-12C2/Nm2)r=8475Nm/C Er= r
Take a very long insulating rod, radius a=0.05m and charge density =60 C/m3, surrounded by a conducting hollow cylinder of inner radius b=0.10m and outer radius c=0.15m. What is the magnitude of E at b < r < c? E =0 ! = q 0 enc E ( )+s 2p bh h ( ) 0= r p a2h r s = -ra2 2b s =-(60mC/m3)(0.05m)2 2(0.10m) =-0.75mC/m2
Same setup: long insulating rod, radius a=0.05m, =60 C/m3 conducting pipe inner and outer radius b=0.10m, c=0.15m, but now with charge =15 C/m. What is the magnitude of E at r > c? = q 0 enc E h ( )= r pa2h ( )+l h e02pr hEr r Er=rpa2+l 2pe0r Er=(60mC/m3)p(0.05m)2+(15mC/m) 2p(8.85 10-12C2/Nm2)r =2.78 105Nm/C r
